On Asymptotically Almost Periodic Generalized Solutions of Differential Equations

2015 ◽  
pp. 35-43
Author(s):  
Chikh Bouzar ◽  
Mohammed Taha Khalladi
Keyword(s):  
Differential Equations ◽  
Generalized Solutions ◽  
Almost Periodic ◽  
Asymptotically Almost Periodic

Existence, Uniqueness and Qualitative Properties of Global Solutions of Abstract Differential Equations with State-Dependent Delay

2019 ◽  
Vol 62 (3) ◽  
pp. 771-788 ◽  
Author(s):  
Eduardo Hernández ◽  
Jianhong Wu
Keyword(s):  
Population Dynamics ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Global Solutions ◽  
Almost Periodic ◽  
Qualitative Properties ◽  
Abstract Differential Equations ◽  
State Dependent ◽  
State Dependent Delay ◽  
Asymptotically Almost Periodic

AbstractWe study the existence, uniqueness and qualitative properties of global solutions of abstract differential equations with state-dependent delay. Results on the existence of almost periodic-type solutions (including, periodic, almost periodic, asymptotically almost periodic and almost automorphic solutions) are proved. Some examples of partial differential equations with state-dependent delay arising in population dynamics are presented.

scholarly journals Ergodicity and asymptotically almost periodic solutions of some differential equations

2001 ◽  
Vol 25 (12) ◽  
pp. 787-801 ◽  
Author(s):  
Chuanyi Zhang
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Nonlinear Differential Equations ◽  
Almost Periodic Solution ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Ergodic Condition ◽  
Asymptotically Almost Periodic

Using ergodicity of functions, we prove the existence and uniqueness of (asymptotically) almost periodic solution for some nonlinear differential equations. As a consequence, we generalize a Massera’s result. A counterexample is given to show that the ergodic condition cannot be dropped.

scholarly journals Asymptotically Almost Periodic Solutions for a Class of Stochastic Functional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Aimin Liu ◽  
Yongjian Liu ◽  
Qun Liu
Keyword(s):  
Differential Equations ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Almost Periodic ◽  
Quadratic Mean ◽  
Exponential Trichotomy ◽  
Functional Differential ◽  
Asymptotically Almost Periodic ◽  
Stochastic Functional

This work is concerned with the quadratic-mean asymptotically almost periodic mild solutions for a class of stochastic functional differential equationsdxt=Atxt+Ft,xt,xtdt+H(t,xt,xt)∘dW(t). A new criterion ensuring the existence and uniqueness of the quadratic-mean asymptotically almost periodic mild solutions for the system is presented. The condition of being uniformly exponentially stable of the strongly continuous semigroup{Tt}t≥0is essentially removed, which is generated by the linear densely defined operatorA∶D(A)⊂L2(ℙ,ℍ)→L2(ℙ,ℍ), only using the exponential trichotomy of the system, which reflects a deeper analysis of the behavior of solutions of the system. In this case the asymptotic behavior is described through the splitting of the main space into stable, unstable, and central subspaces at each point from the flow’s domain. An example is also given to illustrate our results.

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